Nanotechnology-Enabled Sensors

or after rearranging:
83
ΔH
system
ΔS
system − ≥ 0
(3.40)
T
Δ system system
3.4 Electrical Transducers
H − TΔS
≤ 0
(3.41)
In a spontaneous chemical reaction, free energy is released from the system,
causing it to become more thermodynamically stable. The spontaneity
can be deduced by determining the change in free energy available for doing
work, which is called the Gibbs free energy:
ΔG = ΔH – TΔS , (3.42)
where ΔH is the change of the system’s enthalpy, which at constant pressure
is the same as the heat added or removed, T is the temperature, and ΔS
is the change in the systems entropy. The free energy conditions for spontaneity
are:
ΔG < 0, spontaneous (favored) reaction
ΔG = 0, system in equilibrium, no driving force prevails (3.43)
ΔG > 0, non-spontaneous (disfavored) reaction
From the second law of thermodynamics, ΔS of a chemical reaction that
is not in equilibrium will tend to increase. Therefore, to ensure the reaction
is spontaneous (ΔG < 0), from Eq. (3.42) it is observed that ΔH must be
sufficiently negative. If the free energy of the reactants in a chemical reaction
occurring at constant temperature and pressure is higher than that of
the products, Greactants > Gproducts, then the reaction will occur spontaneously.
The Gibbs free energy at any stage of the reaction can be found through
its relationship with the reaction quotient in Eq. (3.29), defined as:
ΔG = ΔG 0 + RTln(QP) , (3.44)
where ΔG 0 is the standard-state free energy of reaction, and R is the gas
constant (8.314472 J·K –1 ·mol –1 ). When the reaction reaches equilibrium,
ΔG = 0 and the reaction quotient takes on the valued of the equilibrium
constant from Eq. (3.30). The change in free energy at equilibrium becomes:
ΔG 0 = –RTln(K) . (3.45)
As will be demonstrated later, this equation is of fundamental importance
to the function of electrochemical sensors. K is a function of analyte